Calculate area of rectangle

Question

Let

 

f(x)= lx-1l

 

g(x)= -lx+1l+4

 

Calculate the area of the rectangle marked by the 2 vertices and the 2 intersections as shown in the plot below.

(Shown in the photo in the link below.)

 

https://hishsaka.smugmug.com/Math/i-7kBBzVJ/A

 

Answer 1

Each of the Squares represents 1 square unit.  There are 2 full squares enclosed within the rectangle formed by the intersection of the graphs.  Each of the triangles represents 1/2 the area of each square, or 1/2 square unit.  There are 8 of these triangles within the rectangle, which amounts to 8 times 1/2, or 4 square units.  Adding the areas of the squares and rectangles within the rectangle, results in a total area of 2 + 4, or 6 square units.